S = \(\dfrac{1}{5^2}+\dfrac{1}{7^2}+\dfrac{1}{9^2}+...+\dfrac{1}{103^2}\) CMR:S ⋮\(\dfrac{5}{32}\)
Giúp em với ạ . Mai em thi rồi ạ
Giúp em với ạ!!!
Thực hiện các phép tính:
a/ \(\dfrac{2}{3}\)+\(\dfrac{1}{5}\).\(\dfrac{10}{7}\)\(\)
b/ \(\dfrac{7}{12}\)-\(\dfrac{27}{7}\)\(\).\(\dfrac{1}{8}\)
c/ \(\dfrac{5}{9}\).\(\dfrac{7}{13}\)\(\)+\(\dfrac{5}{9}\).\(\dfrac{9}{13}\)-\(\dfrac{3}{13}\).\(\dfrac{5}{9}\)
Em cần ngay ạ!!!
\(\dfrac{2}{3}+\dfrac{1}{5}.\dfrac{10}{7}=\dfrac{2}{3}+\dfrac{10}{35}=\dfrac{70}{105}+\dfrac{30}{105}=\dfrac{100}{105}=\dfrac{50}{21}\)
a) Ta có: \(\dfrac{2}{3}+\dfrac{1}{5}\cdot\dfrac{10}{7}\)
\(=\dfrac{2}{3}+\dfrac{2}{7}\)
\(=\dfrac{14}{21}+\dfrac{6}{21}\)
\(=\dfrac{20}{21}\)
\(\dfrac{7}{12}-\dfrac{27}{7}.\dfrac{1}{8}=\dfrac{7}{12}-\dfrac{27}{56}=\dfrac{392}{672}-\dfrac{324}{672}=\dfrac{68}{672}=\dfrac{17}{168}\)
Tìm x :
a)\(\dfrac{49}{81}\)=\(\dfrac{7^x}{9}\) b)\(\dfrac{-64}{343}\)=(\(\dfrac{-4^x}{7}\))
c)\(\dfrac{9}{144}\)=\(\dfrac{3^x}{12}\) d)\(\dfrac{-1}{32}\)=(\(\dfrac{-1^x}{2}\))
Giúp với ạ bài khó quá . Em cảm ơn ạ !
a) \(\dfrac{49}{81}=\dfrac{7^x}{9^x}\)(sửa đề)
\(\Leftrightarrow\left(\dfrac{7}{9}\right)^2=\left(\dfrac{7}{9}\right)^x\)\(\Rightarrow x=2\)
b) \(\dfrac{-64}{343}=\left(-\dfrac{4^x}{7^x}\right)\)(sửa đề)
\(\Leftrightarrow\left(-\dfrac{4}{7}\right)^3=\left(-\dfrac{4}{7}\right)^x\) \(\Rightarrow x=3\)
c) \(\dfrac{9}{144}=\dfrac{3^x}{12^x}\)(sửa đề)
\(\Leftrightarrow\left(\dfrac{3}{12}\right)^2=\left(\dfrac{3}{12}\right)^x\Rightarrow x=2\)
d) \(-\dfrac{1}{32}=\left(-\dfrac{1^x}{2^x}\right)\)(sửa đề)
\(\Leftrightarrow\left(-\dfrac{1}{2}\right)^5=\left(-\dfrac{1}{2}\right)^x\Rightarrow x=5\)
Mong bạn xem lại đề bài.
Bài 1: Thực hiện phép tính: (tính nhanh nếu có thể)
Câu 49. \(7\dfrac{3}{5}-\left(2\dfrac{5}{7}+5\dfrac{3}{5}\right)\)
Câu 50. \(\dfrac{-1}{9}.\dfrac{15}{22}:\dfrac{-25}{9}\)
Giúp em 2 câu cuối với ạ <3
\(49,=\dfrac{38}{5}-\left(\dfrac{19}{7}+\dfrac{28}{5}\right)\)
\(=\dfrac{38}{5}-\dfrac{19}{7}-\dfrac{28}{5}\)
\(=\left(\dfrac{38}{5}-\dfrac{28}{5}\right)-\dfrac{19}{7}\)
\(=2-\dfrac{19}{7}=-\dfrac{5}{7}\)
\(50,=\dfrac{25}{81}.\dfrac{15}{22}=\dfrac{125}{594}\)
Câu 50 tus sửa đề
\(-\dfrac{1}{9}.\dfrac{15}{22}:\dfrac{-25}{9}=-\dfrac{1}{9}.\dfrac{15}{22}.\dfrac{-9}{25}=\dfrac{15}{22}.\dfrac{1}{25}=\dfrac{3}{110}\)
Bài 1 :
Câu 49 . = 38/5 - ( 19/7 + 28/5 )
= 38/5 - 19/7 - 28/5
= ( 38/5 - 28/5 ) - 19/7
= 2 - 19/7 = -5/7
Câu 50 . = ( -1/9 : -25/9 ) . 15/22
= 1/25 . 15/22 = 3/110
Đúng 100 % nha bạn 🤍
Chứng minh S<\(\dfrac{5}{32}\)
Cho \(S=\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{103^2}\)
Bạn Tiểu Tôm Béo ơi có thể check lại đề không ạ?
giúp em với ạ. em cần gấp. camon
Tính bằng cách hợp lí:
a, 2 - (\(\dfrac{3}{7}\)+\(\dfrac{1}{3}\)) - (2- \(\dfrac{4}{3}\)+\(\dfrac{2}{7}\)) + 2 - (4-\(\dfrac{5}{7}\))
b, \(\dfrac{-3}{13}\) . (\(\dfrac{44}{33}\)+\(\dfrac{4444}{3030}\)+\(\dfrac{444444}{404040}\))
\(\dfrac{1}{5+1}\)+\(\dfrac{2}{5^2+1}\)+\(\dfrac{3}{5^3+1}\)+....+\(\dfrac{202}{5^{202}+1}\) < \(\dfrac{1}{4}\)
Chứng minh giúp em ạ!!!
\(\dfrac{1}{5+1}\)
Cho T = \(\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{20^2}\)
So sánh T với \(\dfrac{8}{7}\)
Em cần gấp! Mọi người giúp em với ạ
Ta có \(\dfrac{1}{2^2}< \dfrac{1}{1.2};\dfrac{1}{3^2}< \dfrac{1}{2.3};...;\dfrac{1}{20^2}< \dfrac{1}{19.20}\)
Cộng vế với vế ta được
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{20^2}< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}-\dfrac{1}{20}\)
\(\Rightarrow T< 2-\dfrac{1}{20}=\dfrac{39}{20}\)
mà 39/20 < 8/7 => T < 8/7
1, Tính
\(-2\dfrac{1}{4}.\left(3\dfrac{5}{12}-1\dfrac{2}{9}\right)\)
\(\left(-25\%+0,75+\dfrac{7}{12}\right):\left(-2\dfrac{1}{8}\right)\)
2, Tính nhanh
\(\dfrac{4}{9}.19\dfrac{1}{3}-\dfrac{4}{9}.39\dfrac{1}{3}\) | \(19\dfrac{5}{8}:\dfrac{7}{12}-15\dfrac{1}{4}.\dfrac{12}{7}\)
\(\dfrac{-5}{7}.\dfrac{5}{11}+\dfrac{-5}{7}.\dfrac{2}{11}-\dfrac{5}{7}:\dfrac{11}{14}\) | \(\dfrac{4}{7}.\dfrac{89}{5}-\dfrac{4}{5}.\dfrac{82}{7}\)
\(\dfrac{5}{7}.\dfrac{-4}{19}+\dfrac{-15}{7}.\dfrac{5}{19}\) | \(8\dfrac{2}{7}-\left(3\dfrac{4}{9}+4\dfrac{2}{7}\right)\)
- Giải hộ với ạ, mấy anh, chị lớp 7,8 cũng được huhu :(( sáng mai nộp đề cương rồi. Làm ơn đi a
Muốn gì cũng hậu tạ :>
\(-2\dfrac{1}{4}.\)\(\left(3\dfrac{5}{12}-1\dfrac{2}{9}\right)\)
=\(\dfrac{-9}{4}\).\(\left(\dfrac{41}{12}-\dfrac{11}{9}\right)\)
=\(\dfrac{-9}{4}.\dfrac{41}{12}-\dfrac{-9}{4}.\dfrac{11}{9}\)
=\(\dfrac{-123}{16}-\dfrac{-11}{4}\)
=\(\dfrac{-123}{16}-\dfrac{-44}{16}\)
=\(\dfrac{-79}{16}\)
\(\left(-25\%+0,75+\dfrac{7}{12}\right)\div\left(-2\dfrac{1}{8}\right)\)
=\(\left(\dfrac{-1}{4}+\dfrac{3}{4}+\dfrac{7}{12}\right)\div\left(\dfrac{-17}{8}\right)\)
=\(\left(\dfrac{-3}{12}+\dfrac{9}{12}+\dfrac{7}{12}\right).\dfrac{-8}{17}\)
=\(\dfrac{13}{12}.\dfrac{-8}{17}=\dfrac{-26}{51}\)
\(\dfrac{4}{7}.\dfrac{89}{5}-\dfrac{4}{5}.\dfrac{82}{7}\)
=\(\dfrac{4}{5}.\dfrac{89}{7}\dfrac{4}{5}.\dfrac{82}{7}\)
=\(\dfrac{4}{5}\left(\dfrac{89}{7}-\dfrac{82}{7}\right)\)
=\(\dfrac{4}{5}.1=\dfrac{4}{5}\)
\(\approx\) chúc bạn học tốt \(\approx\)